Method and apparatus for measuring dopant profile of a semiconductor

ABSTRACT

A method and apparatus for measuring dopant profile of a semiconductor is disclosed. Initially, the temperature of a tip of a probe and the temperature of a semiconductor sample are ascertained. Then, a voltage at a location on a surface of the semiconductor sample is obtained via the tip of the probe. The dopant concentration at the location of the surface of the semiconductor sample is subsequently determined by combining the obtained voltage and the temperature difference between the probe tip and the semiconductor sample. The above-mentioned steps can be repeated in order to generate a dopant profile of the semiconductor.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to semiconductor characterization ingeneral, and in particular to a method and apparatus for measuring thedopant profile of a semiconductor. Still more particularly, the presentinvention relates to a method and apparatus for measuring atwo-dimensional dopant profile of a semiconductor.

2. Description of the Prior Art

Present-day integrated circuit manufacturing technology demands accurateknowledge of the concentration of dopants that have been incorporatedinto substrates. This is because dopant concentration within a substratehas a significant effect on the performance of discrete devices, such astransistors, that are built on the substrate. In addition, it is alsoimportant to have the knowledge of the dopant concentration in a spatialextent for process development.

Typically, the active region of a field-effect transistor (FET) isengineered by incorporating dopants, such as arsenic, boron, orphosphorate, in a concentration ranging from 10¹⁵ cm⁻³ to 10²⁰ cm⁻³.When building FETs at a submicron level, it is necessary to quantify thevariation of the above-mentioned dopants at the junction regions ofsubmicron FETs to a resolution of 10 nm or less over four orders ofmagnitude in dopant concentration.

There are several prior art techniques for measuring dopant profiles ofa semiconductor, which include Scanning Capacitance Microcopy, ScanningKelvin Probe Microscopy, Scanning Preading Resistance Microscopy, etc.However, all of the prior art techniques generally do not have a veryhigh sensitivity and/or spatial resolution to meet the demands ofintegrated circuit manufacturing at submicron levels. Furthermore, thesensitivity of some of the prior art techniques tends to decrease as thespatial resolution increases with the usage of sharper probes.Consequently, it would be desirable to provide an improved method andapparatus for measuring dopant profile of a semiconductor.

SUMMARY OF THE INVENTION

In accordance with a preferred embodiment of the present invention, thetemperature of a tip of a probe and the temperature of a semiconductorsample are ascertained. A voltage at a location on a surface of thesemiconductor sample is obtained via the tip of the probe. The dopantconcentration at the location of the surface of the semiconductor sampleis then determined by combining the obtained voltage and the temperaturedifference between the probe tip and the semiconductor sample. Theabove-mentioned steps can be repeated in order to generate a dopantprofile of the semiconductor.

All objects, features, and advantages of the present invention willbecome apparent in the following detailed written description.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention itself, as well as a preferred mode of use, furtherobjects, and advantages thereof, will best be understood by reference tothe following detailed description of an illustrative embodiment whenread in conjunction with the accompanying drawings, wherein:

FIG. 1 is a diagram of an apparatus for measuring dopant profile of asemiconductor, in accordance with a preferred embodiment of the presentinvention;

FIG. 2 is a high-level logic flow diagram of a method for measuringdopant profile of a semiconductor, in accordance with a preferredembodiment of the present invention; and

FIG. 3 is a graph of Seebeck coefficient verses channel location at ap-n junction of a semiconductor.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

The Seebeck coefficient of a semiconductor depends on the concentrationof dopants within the semiconductor. For example, the Seebeckcoefficient S of an n-type silicon is $\begin{matrix}{S = {\frac{1}{{- e}\quad T}\left( {E_{C} - E_{F} + {2k_{B}T}} \right)}} \\{\approx {{- \frac{k_{B}}{e}}\ln\quad\frac{n}{N_{c}}}}\end{matrix}$where

-   -   e=charge    -   T=temperature    -   n=dopant concentration    -   E_(C)=conduction band energy    -   E_(F)=Fermi energy    -   k_(B)=Boltzman constant    -   N_(c)=constant        Thus, the dopant concentration of a semiconductor can be        determined by measuring the Seebeck coefficient of the        semiconductor via        $n = {N_{c}{\exp\left\lbrack {- \frac{eS}{k_{B}}} \right\rbrack}}$        The Seebeck coefficient can be measured by using Scanning        Thermoelectric Microscopy (STEM), as detailed in Ghoshal, Miner        and Majumdar, Proc. 19^(th) , Int. Thermoelectrics        Conference, p. 221 (2000), the pertinent of which is        incorporated herein by reference, or Scanning Chemical Potential        Microscopy (SCPM), as detailed in Williams and Wickramasinghe,        Nature, 344, p. 317 (1990), the pertinent of which is        incorporated herein by reference.

Referring now to the drawings and in particular to FIG. 1, there isdepicted a diagram of an apparatus for measuring dopant profile of asemiconductor, in accordance with a preferred embodiment of the presentinvention. As shown, a silicon sample 12 at temperature T₀ is scanned bya sharp metal probe 11 at temperature T₁. During scanning, thetip-sample gap (i.e., the gap between the tip of metal probe 11 andsilicon sample 12) is regulated by an electron tunneling feedback loopof a Scanning Tunneling Microscope (STM) (not shown). The temperature atthe tip-sample junction is at an intermediate temperature T_(j) thatlies between T₁ and T₀. Ignoring any small thermoelectric voltagedeveloped in metal probe 11, the measured thermoelectric voltage by avoltmeter 10 at a point (x, y) on the surface of silicon sample 12 is${V\left( {x,y} \right)} = {\int_{\infty}^{0}{{S\left( \overset{\_}{r} \right)}{{\nabla\quad{T\left( \overset{\_}{r} \right)}} \cdot {\mathbb{d}r}}}}$where r=distance on silicon sample 12 from the tip of metal probe 11.

Most temperature change occurs within a few factor, m, of tip radiusr_(t) from the tip-sample junction. The dopant concentration and, thus,Seebeck coefficient S is assumed to be constant within mr_(t) from thetip-sample junction of silicon sample 12. Hence, $\begin{matrix}{{V\left( {x,y} \right)} \approx {{S\left( {x,y} \right)}\left( {T_{j} - T_{0}} \right)}} \\{= {{S\left( {x,y} \right)}{\beta\left( {T_{1} - T_{0}} \right)}}}\end{matrix}$where

-   -   T₀ temperature of silicon sample    -   T₁=temperature of metal probe tip    -   T_(j)=temperature of tip-sample junction    -   β=a constant depending on the thermal property of metal probe        and silicon sample, the radius of metal probe tip, tip-sample        junction, etc.

Thus, the Seebeck coefficient at a point (x,y) on the surface of siliconsample 12 can be found by:${S\left( {x,y} \right)} = \frac{V\left( {x,y} \right)}{\beta\left( {T_{1} - T_{0}} \right)}$By substituting S(x,y) into the above-mentioned dopant concentrationequation, the dopant concentration n at a point (x,y) on the surface ofsilicon sample 12 can be found by:${n\left( {x,y} \right)} = {N_{c}{\exp\left\lbrack {- \frac{{eV}\left( {x,y} \right)}{\beta\quad{k_{B}\left( {T_{1} - T_{0}} \right)}}} \right\rbrack}}$Accordingly, dopant profile of silicon sample 12 can be obtained bycontinuously measuring the voltage at various points (x,y) on thesurface of silicon sample 12.

When using an atomically sharp etched tungsten tip having a tip radiusof approximately 1 nm, and if factor m is less than 5, then the spatialresolution of the method of the present invention equals mr_(t)<10 nm.The sensitivity (or concentration resolution) of the method of thepresent invention can be shown as $\begin{matrix}{\frac{\delta\quad n}{n} = {\delta\left( {\ln\quad n} \right)}} \\{= {\frac{e}{k_{B}}\delta\quad S}} \\{= {{\frac{e}{k_{B}\left( {T_{j} - T_{0}} \right)}\left( {{\delta\quad V} + {S\quad{\delta\left( {T_{j} - T_{0}} \right)}}} \right)} \leq {4\%}}}\end{matrix}$with a temperature difference (T_(j)−T₀)=30° K, and voltage δV=1 μV, andtemperature measurement resolution δ(T_(j)−T₀)=0.1° K. Furthermore, themeasured voltage signal does not decrease with tip radius; thus, themethod of the present invention is free from the trade-off betweensensitivity and spatial resolution, which occurs in other dopantprofiling techniques such as Scanning Kelvin Force Probe Microscopy orScanning Capacitance Microscopy.

With reference now to FIG. 2, there is depicted a high-level logic flowdiagram of a method for measuring a two-dimensional dopant profile of asemiconductor, in accordance with a preferred embodiment of the presentinvention. Starting at block 20, the temperatures of a probe tip and asemiconductor sample are initially determined, as shown in block 21. Forexample, the probe can be at ambient temperature that can be measured bya thermometer, and the semiconductor sample can be at a highertemperature than the probe, which can be measured by a thermocouple thatis well-known to those skilled in the art. Then, the voltage at alocation on the surface of the semiconductor sample is obtained via thetip of the probe, as depicted in block 22. The dopant concentration ofthe semiconductor sample at that location can be calculated by combiningthe determined voltage and temperature difference between the probe tipand the semiconductor sample, as shown in block 23. A dopant profile canbe generated by repeating the steps depicted in block 21 through block23, which is to measure the voltage at various locations on the surfaceof the semiconductor sample.

The knowledge of junction geometries are critical for the design offield-effect transistors (FETs) having a channel length of less than 100nm. The method of the present invention is particularly useful indetermining the boundaries of shallow source and drain junctions, andthe profiles near the channel surface of a FET.

Referring now to FIG. 3, there is illustrated a graph of Seebeckcoefficient verses channel location at a p-n junction of asemiconductor. As shown, the Seebeck coefficient profile isdiscontinuous at a p-n junction 30. There is also a sign change at p-njunction 30. The discontinuity is directly related to the band gap ofthe semiconductor and the local temperature (Δ=E_(g)/eT). For silicon,E_(g)=1.1 eV, so that Δ=3.6 mV/° K. The magnitude of Δ is large so thatthe boundaries can be determined accurately.

As has been described, the present invention provides a method andapparatus for measuring a two-dimensional dopant profile of asemiconductor. Although only an n-type silicon is used to illustrate thepresent invention, it is understood by those skilled in the art that theprinciple of the present invention can also be applied to p-type siliconor other types of substrates. For example, the present invention isapplicable to Germanium substrates and Gallium Arsenide substrates.

The present invention takes advantage of the strong dependance ofSeebeck coefficient of a semiconductor on its doping concentration. Assuch, the dopant profile can be obtained by measuring the Seebeckcoefficient variations via Scanning Thermoelectric Microscopy orScanning Chemical Potential Microscopy. The advantages of the method andapparatus of the present invention include superior spatial resolution(better than 10 nm) and better sensitivity (higher than 4%).

While the invention has been particularly shown and described withreference to a preferred embodiment, it will be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention.

1. A method for measuring dopant concentration of a semiconductor, saidmethod comprising: determining temperature of a tip of a probe;determining temperature of a semiconductor sample; determining a voltageat a location on a surface of said semiconductor sample with said tip ofsaid probe; and determining dopant concentration at said location ofsaid surface of said semiconductor sample by${n\left( {x,y} \right)} = {N_{c}{\exp\left\lbrack {- \frac{{eV}\left( {x,y} \right)}{\beta\quad{k_{B}\left( {T_{1} - T_{0}} \right)}}} \right\rbrack}}$where n(x,y)=dopant concentration at location (x,y) on saidsemiconductor sample surface e=charge of electron V(x,y)=voltage atlocation (x,y) on said semiconductor sample surface T₀=temperature ofsaid semiconductor sample T₁=temperature of said tip of said probeK_(B)=Boltzman constant β=constant N_(c)=constant.
 2. The method ofclaim 1, wherein said tip of said probe is controlled by an electrontunneling feedback loop of a Scanning Tunneling Microscope.
 3. Themethod of claim 1, wherein said method further includes a step ofrepeating said determining steps to generate a dopant profile of saidsemiconductor sample.
 4. The method of claim 1, wherein saidsemiconductor sample is a silicon substrate.
 5. The method of claim 1,wherein said semiconductor sample is a germanium substrate.
 6. Themethod of claim 1, wherein said semiconductor sample is a galliumarsenide substrate.
 7. An apparatus for measuring dopant concentrationof a semiconductor, said apparatus comprising: means for determiningtemperature of a tip of a probe; means for determining temperature of asemiconductor sample; means for determining a voltage at a location on asurface of said semiconductor sample with said tip of said probe; andmeans for determining dopant concentration at said location of saidsurface of said semiconductor sample by${n\left( {x,y} \right)} = {N_{c}{\exp\left\lbrack {- \frac{{eV}\left( {x,y} \right)}{\beta\quad{k_{B}\left( {T_{1} - T_{0}} \right)}}} \right\rbrack}}$where n(x,y)=dopant concentration at location (x,y) on saidsemiconductor sample surface e=charge of electron V(x,y)=voltage atlocation (x,y) on said semiconductor sample surface T₀=temperature ofsaid semiconductor sample T₁=temperature of said tip of said probeK_(B)=Boltzman constant β=constant N_(c)=constant.
 8. The apparatus ofclaim 7, wherein said tip of said probe is controlled by an electrontunneling feedback loop of a Scanning Tunneling Microscope.
 9. Theapparatus of claim 7, wherein said semiconductor sample is a siliconsubstrate.
 10. The apparatus of claim 7, wherein said semiconductorsample is a germanium substrate.
 11. The apparatus of claim 7, whereinsaid semiconductor sample is a gallium arsenide substrate.